Average gates before and after stadium moves:
Arsenal: 38,184 (05/06); 60,045 (06/07) - Increase of 22,000.
Man City: 34,564 (02/03); 46,834 (03/04 - City were utter crap this season, finished 16th) - Increase of 12,000.
Sunderland: 20,974 (96/97 - relegated); 33,492 (97/98 - first season in new stadium was in the Championship) - Increase of 13,000.
Derby County: 17,889 (96/97); 29,105 (97/98) - Increase of 12,000.
Middlesbrough: 18,807 (94/95); 29,257 (95/96) - Increase of 11,000.
Bolton: 15,826 (96/97); 24,352 (97/98) - Increase of 9,000.
Southampton: 15,115 (00/01); 30,633 (01/02) - Increase of 15,000.
Leicester: 19,835 (01/02); 29,231 (02/03) - Increase of 10,000.
There's 8 stadiums for you. There's others I can add to the list if you want.
It is a basic given that you open a new stadium, you attract more fans. Anything from 9,000 to 22,000, right here. People are attracted to nice, shiney new things with modern facilities and no posts in the way.
It does guarantee a pretty sizeable increase in home support.